Geometry and measures worksheet — GCSE Foundation

1.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

2.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

3.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

4.Work out the exact value of sin 30° + cos 60°.

5.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

6.Write down the number of lines of symmetry a rhombus has.

7.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?

8.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².

9.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

10.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

11.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

12.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

13.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.

14.How many vertices does a cylinder have?

15.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.